Qinggao Feng

Groundwater drawdown during dewatering of long excavations is influenced by cutoff walls and leakage from adjacent aquitards, yet their coupled transient effects are not fully represented by existing semi-analytical models. We develop a two-dimensional semi-analytical solution for constant-rate pumping in a leaky confined aquifer bounded by a partially penetrating cutoff wall. The formulation accounts for aquifer anisotropy, aquitard storage and vertical leakage, partial penetration of the pumping well, and groundwater exchange beneath the wall. The governing equations are solved using Laplace transformation and separation of variables; numerical Laplace inversion yields time-dependent drawdown. Model predictions are compared with finite-element results, a published non-leaky solution, and pumping test observations from a long excavation in Shanghai. The parameter analyses indicate that deeper wall penetration increases in-pit drawdown while slightly reducing drawdown outside the wall. Lower vertical-to-horizontal hydraulic conductivity ratios intensify the in-pit response. Reducing aquitard hydraulic conductivity or increasing its thickness limits leakage recharge and raises drawdown in both zones, whereas aquitard specific storage primarily influences the timing of the transient response. The results demonstrate that wall geometry and aquitard properties jointly control drawdown magnitude and evolution, and that the proposed solution can support preliminary assessment of dewatering schemes where two-dimensional flow is a reasonable approximation.

In deep excavation dewatering engineering, fully enclosed cutoff walls are widely implemented to improve the efficiency of dewatering in the pit and prevent adverse environmental impacts such as land subsidence and damage to adjacent infrastructure. However, the presence of such impermeable barriers fundamentally alters flow dynamics, rendering conventional aquifer test interpretation methods inadequate. This study presents a novel closed-form analytical solution for transient drawdown in a leaky confined aquifer bounded by a rectangular, fully enclosed cutoff wall under constant-rate pumping. The solution is rigorously derived by applying the mirror image method within a superposition framework, explicitly accounting for the barrier effect of the curtain. A type-curve matching methodology is developed to inversely estimate key aquifer parameters—transmissivity, storativity, and vertical leakage coefficient—while incorporating the geometric and boundary effects of the curtain. The approach is validated against field data from a pumping test conducted at a deep excavation site in Wuhan, China. Excellent agreement is observed between predicted and measured drawdowns across multiple observation points, confirming the model’s fidelity. The proposed solution and parameter estimation technique provide a physically consistent, analytically tractable, and computationally efficient framework for interpreting pumping tests in constrained aquifer systems, thereby improving predictive reliability in dewatering design and supporting sustainable groundwater management in urban underground construction.

Long, narrow, deep excavations commonly encountered in practice, such as those for subway stations, require effective groundwater management to prevent disasters in water-rich areas. To achieve this, a cut-off curtain and pumping well are typically employed during long, deep foundation pit dewatering. The unsteady groundwater flow behavior in the confined aquifer must consider the influence of the cut-off curtain during dewatering. This paper establishes a two-dimensional analytical model to describe transient groundwater flow in a confined aquifer with a cut-off curtain. Both the dewatering well pumped at a steady discharge inside the pit and the cut-off curtain are partially penetrating in the anisotropic confined aquifer. With the help of the Laplace and Fourier cosine transformations, the semi-analytical drawdown solution for the model is derived and validated against numerical solution and unsteady pumping test data. It is shown that the inserted cut-off curtain depth and the structural parameters of the pumping well significantly affect the drawdown inside the pit. Sensitivity analysis reveals that, regardless of whether the observation is made inside or outside the curtain, the drawdown is very sensitive to the change in pumping rate, aquifer thickness, storage coefficient, and horizontal hydraulic conductivity. Additionally, drawdown near the cut-off curtain outside the pit is sensitive to the vertical hydraulic conductivity of the aquifer, the width of the pit, and the interception depth of the cut-off curtain, while drawdown far from the curtain outside the pit is not sensitive to the location and length of the well screen.

An analytic model for depicting non-Darcian flow caused by pumping in a finite confined aquifer with an outer barrier boundary is established. The model considers the wellbore storage and skin effect. And the semi-analytical solution is derived with the aid of the Izbashs law-based non-Darcian flow and the method for linearization procedure combined with the Laplace transformation. The new presented solution can reduce to some available solutions for the confined aquifer of unlimited extension. The drawdowns in abstraction well and aquifer are explored. The results suggest that the presence of the no-flux outer boundary makes no difference to the early-time drawdowns, the late-time drawdowns in the unlimited confined aquifer are smaller than those in the finite confined aquifer with a zero-flux outer boundary, and the flow in this finite confined aquifer cannot approach quasi-steady state, especially to a smaller finite outer boundary distance radius. The change of power index n in the non-Darcian flow equation cannot affect the early-time drawdowns in abstraction well, while the drawdowns in aquifer are underestimated for Darcian flow case at early pumping time. The late-time drawdowns in the pumping well and aquifer are significantly overestimated under the assumption of Darcian flow. The early-time drawdowns in abstraction well and aquifer are significantly affected by wellbore storage, and a larger wellbore storage coefficient leads to a smaller drawdown. The skin factor can impact the intermediate-time drawdowns in abstraction well, while the early and intermediate-time drawdowns in aquifer are influenced by skin effect.

The mobilization of side resistance has a significant effect on load-transfer characteristics and the ultimate bearing capacity of rock-socketed piles. A good understanding of the shear mechanism of a concrete–rock interface has a critical part in analytical load-transfer solutions of rock-socketed piles. However, most of the existing analytical solutions have ignored the effect of bond strength, which constrains the concrete–rock interface. The present analytical model is distinguished by adopting a modified shear constitutive law of bonded concrete–rock interface. It also considers the wear model of asperity roughness to calculate the critical shear displacement. The accuracy of the analytical formulation is verified by comparison with field cases. Parameters analysis results indicate that the peak shear stress would be improved due to contact bonding. The residual shear stress displays a marked reduction with increasingly unconfined compressive strength of rock under the condition of bond strength consideration.